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For $X,Y\in {𝐌}_{n,m}$, it is said that $X$ is majorized by $Y$ (and it is denoted by $X{\prec }_{gt}Y$) if there exists a tridiagonal g-doubly stochastic matrix $A$ such that $X=AY$. In this paper, the linear preservers and strong linear preservers of ${\prec }_{gt}$ are characterized on ${𝐌}_{n,m}$.